The well known addition formula is given
by (see [1]} and [2]})
\(\sum _{l=1}^{D_k^{d-1}}Y_{k,l}(\xi )Y_{k,l}(\eta )=\frac{2k+d-2}{(d-2)\Omega _{d-1}}G_k^{\frac{d-2}{2}}(\xi \cdot \eta )=K_n^*(\xi \cdot \eta ),\) 
